Self-consistent description of vector-mesons in matter

We study the influence of the virtual pion cloud in nuclear matter at finite densities and temperatures on the structure of the rho- and omega-mesons. The in-matter spectral function of the pion is obtained within a selfconsistent scheme of coupled Dyson equations where the coupling to the nucleon and the Delta(1232)-isobar resonance is taken into account. The selfenergies are determined using a two-particle irreducible (2PI) truncation scheme (Phi-derivable approximation) supplemented by Migdal's short range correlations for the particle-hole excitations. The so obtained spectral function of the pion is then used to calculate the in-medium changes of the vector-meson spectral functions. With increasing density and temperature a strong interplay of both vector-meson modes is observed. The four-transversality of the polarisation tensors of the vector-mesons is achieved by a projector technique. The resulting spectral functions of both vector-mesons and, through vector dominance, the implications of our results on the dilepton spectra are studied in their dependence on density and temperature.